Question: The grades on a math midterm at Covington are normally distributed with $\mu = 68$ and $\sigma = 3.5$. Emily earned a $76$ on the exam. Find the z-score for Emily's exam grade. Round to two decimal places.
Solution: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Emily's exam grade by subtracting the mean $(\mu)$ from her grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{76 - {68}}{{3.5}}} $ ${ z \approx 2.29}$ The z-score is $2.29$. In other words, Emily's score was $2.29$ standard deviations above the mean.